Proton Glass Dielectric Susceptibility
Compared with Monte Carlo and Bound
Charge Semiconductor Model Predictions
Authors: V.H. Schmidt, Z. Trybula, D. He, J.E.
Drumheller, C. Stigers, Z. Li, and F.L. Howell
This is an Accepted Manuscript of an article published in Ferroelectrics in June 1990, available
online: http://www.tandfonline.com/10.1080/00150199008214569.
Schmidt, V. H., Z. Trybula, D. He, J. E. Drumheller, C. Stigers, Z. Li, and F. L. Howell. “Proton
Glass Dielectric Susceptibility Compared with Monte Carlo and Bound Charge Semiconductor
Model Predictions.” Ferroelectrics 106, no. 1 (June 1, 1990): 119–124.
doi: 10.1080/00150199008214569.
Made available through Montana State University’s ScholarWorks
scholarworks.montana.edu
Ferroelecrrics, 1990, Vol. 106, pp. 119-124
Reprints available directly from the publisher
Photocopying permitted by license only
0 1990 Gordon and Breach Science Publishers S.A.
Printed in the United States of America
PROTON GLASS DIELECTRIC SUSCEPTIBILITY COMPARED WITH
MONTE CARL0 AND BOUND CHARGE SEMICONDUCTOR MODEL
PREDICTIONS
V.H. SCHMIDT, Z. TRYBUCA, D. HE, J.E. DRUMHELLER, C.
STIGERS, Z. LI, and F.L. HOWELL*
Physics Dept., Montana State Univ., Bozeman, MT
59717
*Physics Dept., U. North Dakota, Grand Forks, ND
58202
Abstract Our latest results for dielectric
permittivity and loss and protonic conductivity in
RADP, RADA and DRADA proton glasses are presented.
Improvements in our "bound charge semiconductor"
model for dielectric behavior are discussed. Monte
Carlo studies of the phase diagram and polarization
decay are described. Bias order parameter c.
temperature plots from the simulation and from ND,
deuteron NMR lineshapes are compared.
We describe here our proton glass dielectric measurements,
and their interpretation by Monte Carlo simulations based on
a short-range-interaction model and by an analytic model €or
diffusion of effective charge carriers.
We made dielectric measurements on 50% ammoniated
rubidium dihydrogen phosphate (RADP) between 93 and 3 4 8 K.
The losses in this temperature range are caused by protonic
conductivity, which is plotted in Fig. 1. The conductivity
is similar to that of other crystals in this family.
The inverse permittivity plotted in Fig. 2 gives a
straight Curie-Weiss plot for E, near 5. The Curie-Weiss
constant is 2800 K, close to the Slater' theory value of
= 2700 K.
a*~P,~/4ke,
Dielectric results are presented also for 20% ammoniated
rubidium dihydrogen arsenate (RADA), in Figs. 3 and 4. These
show typical proton glass behavior, similar to our results in
35% ammoniated RADA.' However, the 4% ammoniated crystal
shows unusual behavior. In Fig. 5 the ferroelectric
transition at 80 K is followed by typical proton glass
dispersion below 30 K, as seen also in Fig. 6 and in the loss
curves of Fig. 7. We believe that local regions with high Rb'
concentrations are ferroelectric, while NH,'-rich regions show
proton glass behavior.
[ 11911955
b0 '
I
I
I
C = 2 8 0 0 i 600 K
..
IO'/T
FIGURE 1 Conductivity
along's of 50150 RADP.
50
r$J
&p
a
OO
,o o o o o
'roo
I
O=I kHz
I
0 = 3 0 hHz
200
I00
T(K)
1
I
FIGURE 2 Curie-Weiss
behavior of 50150 RADP.
10
300
FIGURE 3 Permittivity
along 5 of 80120 RADA.
I60
T(K)
I
20
T
30
(to
FIGURE 4 Loss along
of
80120 RADA.
a
I
I
I
I
I20
E:
80
0
00
OQ3
000
L(0
0
FIGURE 5 Permittivity along 5 of 9 6 / 0 4 RADA, showing
both ferroelectric transition and dielectric dispersion.
YO
PROTON GLASS DIELECTRIC SUSCEPTIBILITY
...
[ 121]/957
6
0
q
E;
2
0
I
along
I
20
I
I
YO
T (KI
I
I
60
FIGURE 6
a
Permittivity
of 9 6 / 0 4 RADA.
0
T
40
IK)
FIGURE 7 Loss along
of
9 6 / 0 4 RADA.
a
-
T(k)
T(K1
FIGURE 8 Permittivity
along a of 72/28 DRADA.
20
-a
FIGURE 9 Loss along
of 72/28 DRADA.
[122]/958
V. H. SCHMIDT et al.
We made the first dielectric measurements on
deuterated rubidium/ammonium dihydrogen arsenate (DRADA),
on a 28% ammoniated crystal. The results shown in Figs. 8
and 9 resemble those found by Courtens3 in DRADP, because
both DRADA and DRADP show considerable frequency dispersion
in this region, while undeuterated RADA and RADP do not.
We are analyzing this dielectric behavior in terms of
our Ilbound charge semiconductor" model4 I in which
polarization change results from drift of HP04 and H3P04
carriers in an effective field which is the sum of the
applied and configurational fields. The relaxation time
spread results from mobility being a function of time t
after step cutoff of an applied dc field. The polarization
decay from initial value Pi along the c axis obeys
where n is fractional carrier density, To is Curie-Weiss
temperature, €4 is rms diffusion step energy change, To is
attempt time, and 7 is t for small t and approaches a fixed
value for large t. This expression includes the dc
susceptibility proposed by Sherrington and Kirkpatrick, in
which the bias order parameter q is evaluated using the
expression derived by Pirc, Tadib, and Blinc.7
An earlier version of our model8'' gave loss peaks E.
temperature which were too broad. In the present model,
the power of the logarithm in Eq. (1) is 4 instead of 2,
and in its argument t is replaced by 7 which becomes
constant at large t. Both changes narrow the range of
mobility as t increases, and should fit experiment better.
The Monte Carlo simulations are based on a model10,ll
employing short-range interactions and random bias. We can
simulate polarization decay from a state with initial
ferroelectric order (Fig. 10) or antiferroelectric order.
To find the Edwards-Anderson order parameter we record a
proton configuration,let the system evolve, and find the
correlation of the new configuration with the previous one.
m~
2 2-;
::
z ?:I
P
= Seed
":.4
D
-= N O BIAS
- - - = BIAS
FIGURE 11 Monte Carlo determination of phase diagram
for a proton glass model, showing phase boundaries with and
without a random bias field.
0.V
g -
$3 '
I
100
RIA~S
I
T(K1
ORDER'PAR.
I
200
FIGURE 12 Monte Carlo determination of bias order
parameter for a proton glass model, compared with values
found (Ref. 1 2 ) by deuteron NMR artd theory for 5 6 / 4 4 DKADP.
V. H. SCHMIDT et al.
We find the bias order parameter similarly, but warm and then
cool the system so it loses memory of the particular potential minimum it may have been trapped in.
To find the phase diagram, we assume the system is in
the ferroelectric or antiferroelectric state if it retains 90%
of such initial order after a long running time. We found the
phase diagram both with and without random bias, as shown in
Fig. 11. The bias widens the proton glass concentration
range, as expected, because in the NaCN/KCN system which has
no frustration, random bias alone produces a phase diagram
similar to that of proton glass systems.
vs. temperature from
We found the bias order parameter our Monte Carlo simulation and compared it to that found from
deuteron NMR of ammonium deuterons in DRADP proton glass,” as
shown in Fig. 12. The agreement is quite good.
In summary, we have shown new dielectric results, particularly for arsenate proton glasses. Our Monte Carlo and bound
charge carrier models which are based on the crystal structure
and interactions explain these results well.
This work was supported by NSF Grant DMR-8714487.
[124]/960
REFERENCES
1. J. C. Slater, J. Chem. Phys. 9, 16 (1941).
2. Z. Trybula, V. H. Schmidt, J.-E. Drumheller, D. He, and
2. Li, Phys. Rev. B 4 0 , 5289 (1989).
3. E. Courtens, Phys. Rev. B 33, 2975 (1986).
4. V. H. Schmidt, Bull. Am. Phys. SOC. 34, 827 (1989).
5. V.H. Schmidt, Proc. Ramis Conf., Poznafi (April 1989).
6. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35,
1792 (1975).
7. R. Pi&,
B: TadiC, and R. Blinc, Phys. Rev. B 36, 8607
(1987).
8. V. H. Schmidt, Ferroelectrics 3,207 (1988).
177, 257 (1988).
9. V. H. Schmidt, J. Molec. Struc. 10. V. H. Schmidt, J. T. Wang, and P. T. Schnackenberg, Jpn.
J. Appl. Phys. 2 4 , Suppl. 24-2, 944 (1985).
11. V. H. Schmidt, Ferroelectrics 72, 157 (1987).
12. R. Blinc, J. Dolinsek, V. H. Schmidt, and D. C. Ailion,
Europhys. Lett. 5, 55 (1988).